Physical factors dominating milling effect of ball mill milling equipments include dimension (radius r) and rotational speed rpm in regard to a ball mill container. In regard to beads, amount of filled beads (this is expressed in ratio Hb/r of depth Hb of filled beads to radius r (cm) of the ball mill container, or the ratio of the beads to the internal volume of the container), or material, diameter and shape (spherical, cylindrical, etc.) of the beads may be mentioned. Among these physical factors, it is known that consumption power becomes maximum and the best milling efficiency is obtained in case where the amount of filled beads which is expressed in Hb/r is 1.0 (corresponds to 50% based on the internal volume of the ball mill container).
However, in case where the amount of filled beads is as little as 30% or less (Hb/r of 0.6 or less), the balls start to slide along the inner wall of the container to cause remarkable damages to the inner wall. Therefore, in the actual production process, the amount of beads is generally kept to one third to half of the total volume of the ball mill container (Hb/r of 0.66 to 1.0).
In the milling by a ball mill, the balls are gradually lifted highly in the rotational direction with the movement of the mill, and the ball is involved in a snowslide motion together with a plenty of balls when the balls are lifted at the position where there is no support below the balls. Consequently, the balls slide and fall on the surface of the balls and fall below the mill while they collide here and there (snowslide phenomenon).
When the rotational speed is increased, the balls come to fall like a waterfall in the space filled with vapor, rather than the snowslide phenomenon (waterfall phenomenon).
When the rotational speed is further increased, the mill comes to be rotated while the balls are adhered to the inner wall of the mill due to centrifugal force (adhesion phenomenon/adhesion state).
It is clear that no dispersion is achieved in the adhesion state (the balls do not move relatively with the mill). In addition, in the state of the waterfall phenomenon, the balls and the inner wall of the mill have many damages, and dispersion is insufficient. Therefore, these phenomena are undesirable states, and the dispersion of pigments is carried out very efficiently in only the state of snowslide phenomenon which is regarded as an ideal state.
In regard to the rotational speed of the container, it is stated that the optimum rotational speed N0=(203−0.60r)/r1/2 wherein the unit of r is cm (RPM0=(37−3.3r)/r1/2 wherein the unit of r is feet) at the point of which the snowslide phenomenon occurs is an ideal state in the milling by a ball mill (see, for example “Paint Flow and Pigment Dispersion” written by Temple V. Patton, translation supervised by Kenji Ueki., Kyoritsu Shuppan Co., Ltd., 1971, pp. 202-222). This publication states that the above-mentioned equation expressing the optimum rotational speed N0 at the point of which the snowslide phenomenon occurs is obtained in case where the critical rotational speed Nc=60g1/2/2πr1/2=299/r1/2, and is derived from N0=(0.68−0.22r)Nc (rpm0=(0.68−0.06r)rpmc wherein the unit of r is feet). In addition, the publication states that the actual production process is generally carried out in the amount of filled beads and the rotational speed of the container as mentioned above.
In addition, it is stated that the milling of aluminum hydroxide powder is carried out in a ball mill made of stainless steel having a diameter of 78 mm to 199 mm by means of steel beads having a diameter of 10.2 mm (see, for example, “Chemical Equipment” written by Sumiya Kano, Hiroshi Mio and Fumiyoshi Saito, 2001, No. 9, pp. 50-54). This publication reports the test results in which the milling condition is as follows: bead-filling rate of 20 to 80% and number of revolutions of 0.6 to 1.3 time the critical rotational speed. As a result of it, it is stated that milling rate becomes maximum when the bead-filling rate is 40 to 80% and number of revolutions is 80% of the critical rotational number, and the milling rate is increased with an increase in bead diameter, and the milling rate is lowered when the bead-filling rate is beyond 60%.
In the meanwhile, cerium oxide particles are widely used as polishing agent for substrates containing silica as main component, and recently there is a strong demand for cerium oxide polishing agent by which a polished face with a high quality can be obtained without surface defects such as scratch. On the other hand, it is also required strongly to maintain a high removal rate so as not to decrease the productivity. Therefor unmilled large particles causing scratch and over-milled fine particles causing a lowering in removal rate must be reduced in the number in cerium oxide particles to the utmost. That is, it is required a production method by which the particle size distribution of cerium oxide particles can be controlled in order to make it further sharp.
Cerium oxide particles have been finely divided by milling with ball mill using a milling medium such as partially stabilized zirconia oxide beads or alumina beads. However, as these beads are very hard for cerium oxide and milling condition which is generally achieved for milling it is too vigorous, particle size distribution of cerium oxide fine particles becomes very broad.
The present invention resolves this problem and provides a milling method for obtaining cerium oxide particles with a narrow particle size distribution. The cerium oxide particles obtained according to the present invention have a narrow particle size distribution. Therefore, in case where it is used for polishing, it provides a polished face with a high quality without lowering in removal rate, and thus it makes possible to improve the production efficiency and lower the cost.